Dear Colleagues, I am in need for a "divergence metric" that would render Bayesian updating a continuous operator; i.e.,
if D(p,q) is the divergence between distributions p and q, and p^e is the result of updating p with evidence e: p^(e)[i] = p[i] P(e|i) / \sum_j p[j] P(e|j) where P(.|.) doesn't depend on p. Then, I would like to have (1) D(p^e,q^e) <= K*D(p,q) where K is a constant (preferable less than one). In addition, I need that D(.,.) to be a metric in the space of distributions; i.e, (2) D(p,q) = 0 iff p = q, (3) D(p,q) = D(q,p), (4) D(p,q) <= D(p,r) + D(q,r) It is easy to see (with a counterexample) that the symmetric Kullback-Leibler divergence doesn't satisfy (1). I wonder if such D(.,.) exists. Thanks in advance Blai Bonet
